Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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1 - 10
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61 - 70
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101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
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251 - 260
261 - 270
271 - 280
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parameter be equall to K R: and
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let D S be Seſquialter of K R: but
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S B is alſo Seſquialter of B R:
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Therefore, draw a Line from A to
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B; and thorow C draw C E Per
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pendicular to B D, cutting the Line
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A B in the Point E; and thorow E
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draw E Z parallel unto B D. Again,
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A B being divided into two equall
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parts in T, draw T H parallel to the
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ſame B D: and let Sections of
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Rightangled Cones be deſcribed, A E I about the Diameter E Z;
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and A T D about the Diameter T H; and let them be like to the
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Portion A B L: Now the Section of the Cone A E I, ſhall paſs
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thorow K; and the Line drawn from R perpendicular unto B D,
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ſhall cut the ſaid A E I; let it cut it in the Points Y G: and
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thorow Y and G draw P Y Q and O G N parallels unto B D, and
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cutting A T D in the Points F and X: laſtly, draw P
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and O X
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touching the Section A P O L in the
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P
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oints P and O. </
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<
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>In regard,
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therefore, that the three
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P
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ortions A P O L, A E I, and A T D are
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contained betwixt Right Lines, and the Sections of Rightangled
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Cones, and are right alike and unequall, touching one another, upon
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one and the ſame Baſe; and N X G O being drawn from the
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P
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oint N upwards, and Q F Y P from Q: O G ſhall have to G X
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a proportion compounded of the proportion, that I L hath to L A,
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and of the proportion that A D hath to DI: But I L is to L A,
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as two to five: And C B is to B D, as ſix to fifteen; that is, as two
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to five: And as C B is to B D, ſo is
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E B to B A
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; and D Z to
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D A: And of D Z and D A, L I and L A are double: and A D
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is to D I, as five to one:
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B
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ut the proportion compounded of the
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proportion of two to five, and of the proportion of five to one, is
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the ſame with that of two to one: and two is to one, in double
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proportion: Therefore, O G is double of GX: and, in the ſame
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manner is P Y proved to be double of Y F: Therefore, ſince that
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D S is Seſquialter of K R;
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B S
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ſhall be the Exceſs by which the
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Axis is greater than Seſquialter of the Semi-parameter. </
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<
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>If there
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fore, the
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P
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ortion have the ſame proportion in Gravity unto the
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Liquid, as the Square made of the Line
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B S,
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hath to the Square
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made of
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B D,
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or greater, being demitted into the Liquid, ſo as hat
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its
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B
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aſe touch not the Liquid, it ſhall ſtand erect, or perpendicular:
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For it hath been demonſtrated above, that the
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P
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ortion whoſe
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Axis is greater than Seſquialter of the Semi-parameter, if it have
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not leſser proportion in Gravity unto the Liquid, than the Square </
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